Question
Factor (a^2+a)^2-8(a^2+a)+12
Answer
Let b = a^2+a
The original expression is converted to
(a^2+a)^2-8(a^2+a)+12
=b^2-8b+12
=(b-2)(b-6)
Substitute b and continue factoring
(a^2+a-2)(a^2+a-6)
(a+2)(a-1)( a+3)(a-2)
Factor (a^2+a)^2-8(a^2+a)+12
Let b = a^2+a
The original expression is converted to
(a^2+a)^2-8(a^2+a)+12
=b^2-8b+12
=(b-2)(b-6)
Substitute b and continue factoring
(a^2+a-2)(a^2+a-6)
(a+2)(a-1)( a+3)(a-2)